Journal of Mechanical Science and Technology 29 (5) (2015) 2025~2034 www.springerlink.com/content/1738-494x

DOI 10.1007/s12206-015-0423-4

Influence of stator vane number on performance of the axial-flow pump† Can Kang1,*, Xiaojie Yu1, Weifeng Gong2, Changjiang Li2 and Qifeng Huang3 1

School of Energy and Power Engineering, Jiangsu University, Zhenjiang, 212013, China 2 Shanghai Marine Equipment Research Institute, Shanghai, 200031, China 3 Shanghai Kaiquan Pump Group Co., Ltd, Shanghai, 201804, China

(Manuscript Received September 17, 2014; Revised January 21, 2015; Accepted January 29, 2015) ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract The interplay of impeller and stator is investigated for an axial-flow pump. Three stator vane numbers of 5, 7 and 9 are devised to match the same impeller. The renormalization group k-ε turbulence model is used to simulate three-dimensional flows in three pumps with different vane numbers. Axial velocity distributions at impeller outlet and stator outlet are comparatively analyzed. Experiments assess operation performance of the three pumps. Vibration parameters and static pressure fluctuations are measured as well. It is indicated that the influence of vane number on both pump head and pump efficiency is insignificant. Large stator vane number contributes to the improvement of the uniformity of axial velocity distribution at impeller outlet. At stator outlet, similar tendency is revealed. Severe vibration occurs near the outlet bend of the pump, as is particularly remarkable at vane number of 9. For the three cases, blade passing frequency and its harmonics are predominant in the frequency spectra of pressure fluctuations. As flow rate increases from 0.8Q to 1.0Q, high-frequency pressure fluctuations are suppressed considerably at vane number of 9, while the other two cases also manifest a decline in overall pressure fluctuation amplitude. The 7-vane case is the most preferable one among the three cases in terms of both pump performance and pressure fluctuation between the impeller and the stator. Keywords: Axial-flow pump; Stator vane number; Numerical simulation; Performance test; Vibration; Pressure fluctuation ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

1. Introduction With high specific speed and outstanding capability of delivering working medium with large volume flow rate, the axialflow pump has been widely used in military, marine, agricultural and bio-medical fields. In most cases, axial-flow pumps are installed vertically, which is prone to trigger adverse consequences such as vibration and failure of upper bearings [1]. In addition, structural characteristics of the axial-flow pump are complicated with the participation of turbulent flow. In recent years, vibration sources nurtured in inner flows of the impeller pump have gained much attention, and it has been verified in some cases that static pressure fluctuations and pump vibration share typical frequencies [2]. Most of these frequencies are harmonics of shaft frequency or blade passing frequency. The axial-flow pump is featured by unsteady flows between impeller blades and stator vanes. Although numerous efforts have been dedicated to the impeller–stator interaction in the axial-flow pump, a clear explanation of this subject is still sorely necessitated [3]. Furthermore, issues like transient fluid forces exerted on pump components have also been ascribed *

Corresponding author. Tel.: +86 511 88780217, Fax.: +86 511 88780216 E-mail address: [email protected] † Recommended by Associate Editor Donghyun You © KSME & Springer 2015

to the periodic interaction between rotating impeller blades and stationary stator vanes [4]. This is because the working medium discharged from the impeller has been energized and possesses a large portion of total fluid kinetic energy. The mixing of this part of fluid and adjacent fluid with a relatively low level of fluid kinetic energy is conceivably intense [5]. In this context, stator vane number plays an apparently important role with its immediate effect on the periodicity of impellerrotor interaction. Gülich investigated various combinations of impeller blade number and stator vane number and proposed a formula relating these two parameters [6]. For axial-flow gas turbines and compressors, another two important branches of impeller machinery, rotor-stator interaction has been investigated extensively [7, 8]. Explicit pressure spectra obtained in relevant experiments indicate that characteristic frequencies in the flow field between the rotor and the stator correspond well to the rotational frequencies of impeller blades. In contrast, for the axial-flow pump, inconvenience is triggered by the liquid medium instead of gas medium. Thus the design of a suitable test rig often makes many experimental schemes difficult to implement, so generalizable conclusions have rarely been reported hitherto [9]. For instance, optical measurement of the flow between impeller blades and stator vanes seems impracticable in view of the demanding

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configuration of optical transmitters and receivers [10]. With vertical installation of the axial-flow pump, such a measurement is even questionable to accomplish [11]. Under such a circumstance, pressure fluctuations, which could be obtained through pressure transducers mounted on the pump casing, are frequently used to describe flow characteristics. Details of turbulent flows in the axial-flow pump may also be revealed by using numerical simulation, an aggressively popular technique which has been used to disclose diverse flow structures inside impeller pumps. Years of experience enable considerable advancement in both computation ability and the reliability of numerical results. With numerical simulation, the accuracy of resultant averaged flow parameters and hydraulic losses is ensured. Nevertheless, for time-dependent parameters such as fluctuating velocity and pressure obtained numerically, experimental validation is still badly needed. In some cases, even with the same set of boundary and initial conditions, different commercial computational fluid dynamics (CFD) codes might yield obviously different unsteady flow patterns [12]. In essence, spatial and temporal scales required for illustrating the instantaneous effect of flow structures on pump vibration are exceedingly small, which often discourages the application of such an instrument. Our major concern is the effect of stator vane number on pump performance. Pump performance considered here incorporates inner flow feature, working capability of the pump, pump vibration and static pressure fluctuation. To probe into such a subject, numerical simulation is used as a preliminary technique in seeking flow features immediately downstream of the impeller and the stator as well. For comparison, pump head and pump efficiency are measured for cases incorporating different vane numbers. Pump vibration is examined with vibration acceleration sensors attached to both the supporting plate of the pump and the motor base. High-frequency dynamic pressure sensors are used to measure static pressure fluctuations between the impeller and the stator. And the results will account for how the local flow reacts to the periodically changed solid boundaries. Both flow and pump vibration characteristics are supposed to be demonstrated as vane number varies. This study is anticipated to provide a further insight into axial-flow pump performance, as well as inner flow characteristics in the pump with different combinations of impeller blades and stator vanes.

2. Numerical model 2.1 Geometrical parameters and computational domain Under nominal operation condition, the volume flow rate Q of the axial-flow pump considered is 840 m3/h, and the corresponding pump head H is 5.2 m. The impeller spins at the rotational speed n of 1470 rpm. Therefore, the value of specific speed ns of the pump is 206 based on the definition ns =

n ´ Q / 3600 . H 0.75

(1)

Table 1. Primary geometrical parameters of the axial-flow pump. Inlet diameter (mm)

300

Outlet diameter (mm)

300

Impeller diameter (mm)

300

Hub diameter (mm)

150

Impeller blade number Z

4

Stator vane number Z1

5, 7, 9

(a)

(b)

Fig. 1. Three-dimensional models for the 7-vane case: (a) hydraulic components; (b) major computational subdomains.

Generally, empirical approaches are used in the design of the impeller pump to yield preliminary results which are then validated or optimized using CFD or experimental techniques [13]. The streamline method was adopted to design the pump impeller and the three stators. With such a method, variation of circulation from the impeller hub to blade tip can be geared towards an optimal distribution. Stator vanes were designed based upon impeller blade parameters [14]. Primary geometrical parameters of hydraulic components are listed in Table 1. All the three vane numbers-5, 7 and 9-conform to the general knowledge of vane number selection. Most treatises relevant to this procedure only suggest a consideration of excessive frictional loss as large vane number is employed, but detailed comparisons in vane number have rarely been documented [15]. Three-dimensional geometrical models of the hydraulic components associated with the 7-vane case are presented in Figs. 1(a) and (b). The subdomains shown in Fig. 1(b) do not include an auxiliary outlet straight subdomain, which is indispensable for full development of turbulent flow. Unstructured grids were employed to discretize computational subdomains associated with impeller blade passages and stator vane passages. Such a grid type can well accommodate irregular solid surfaces such as impeller blade and stator vane surfaces. To improve the accuracy of numerical simulation and to detect small-scale flow phenomena residing in local flows, grid refinement was executed for impeller and stator computational subdomains. In line with the commonly adopted approach evaluating the effect of grid number, a grid-

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production term connected with viscous force. The other constants involved in Eqs. (2)-(4) are: Cm = 0.0845， Ce 1 = 1.42， Ce 2 = 1.68，

s k = 0.72， s e = 0.75.

In general, in flow regions with low strain rates, h < h0 , eddy viscosity calculated with the RNG k-ε model is higher than that obtained with the standard k-ε model, and this tendency is overturned in high-strain-rate flow regions signified by h > h0 . In the presence of both high strain rate and largecurvature solid walls, advantages of the RNG k-ε model are prominent. Fig. 2. Variation of pump head with grid number.

2.3 Discretization strategy and definition of boundary conditions

r

¶ Dk = Dt ¶xi

éæ m êçç m + t sk ëêè

ö ¶k ù ú + Gk - re , ÷÷ ø ¶xi ûú

(2)

The commercial CFD code ANSYS-CFX served as a basic platform for the numerical work covered in the present study [18]. Central finite difference scheme was adopted to treat the convection terms involved. Discretization of momentum and turbulent kinetic energy equations is accomplished using second-order upwind scheme. Velocity inlet boundary conditions were set at the inlet of the whole computational domain and thus the magnitude of flow rate could be adjusted accordingly. The opening boundary condition in ANSYS-CFX was set at the outlet of the whole computational domain. Such a boundary condition is used when flow parameter distributions at the outlet of the whole computational domain are not well understood. As working medium flows out of the computational domain, pressure is treated as static pressure. While recirculation occurs there, pressure is treated as total pressure. Non-slip condition was applied for all solid boundaries. Scalable wall functions were defined in near-wall flow regions. At the interface between the impeller and the stator, the frozen-rotor interface condition was specified. Such an interface condition is a reliable steady-state strategy with fluxes changing frame while the relative orientation of relevant components keeps invariant.

r

De ¶ = Dt ¶xi

éæ m êçç m + t se ëêè

ö ¶e ù e e2 * , ú + Ce 1 Gk - Ce 2 r ÷÷ k k ø ¶xi ûú

(3)

3. Steady simulation results

(4)

Two positions, impeller outlet and stator outlet, suffer directly from the effect of vane number, so do local flows involved. In view of currently attainable accuracy of numerical simulation, only averaged flow information is extracted and analyzed here. For the axial-flow pump, axial velocity component is of remarkable significance. Thus cross-sectional distributions of axial velocity immediately downstream of the impeller and the stator are constructed based upon the obtained numerical results. Relative velocity distributions at impeller outlet are shown in Fig. 3 and absolute velocity distributions at stator outlet are shown in Fig. 4. In both figures, positive velocity values denote the flow direction opposite to the movement of main stream. As indicated in Fig. 3, at a given vane number, the flow rate

independence examination was performed. Grid number was determined after the difference of pump head between two neighboring grid number schemes was less than 1%, as shown in Fig. 2. Grid numbers involved in the final computation are 4671378, 5439416 and 6178812, which correspond to 5-vane, 7-vane and 9-vane cases, respectively. 2.2 Governing equations The renormalization group (RNG) k-ε turbulence model, first proposed by Yakhot and Orszag in 1986, indicates an improvement relative to the standard k-ε turbulence model [16]. This model embodies fuzzy mathematics principles, and the parameters involved in this model are determined according to relevant formulae rather than empiricism or experiments. Along this line, the equation of turbulent kinetic energy dissipation rate ε differs from its counterpart incorporated in the standard k-ε turbulence model. The transport equations of turbulent kinetic energy k and ε are:

and the variable Ce*2 in Eq. (3) is defined as æ h ö Cm rh 3 ç1 - ÷ h 0 ø è , Ce*2 = Ce 2 + 1 + 0.012h 3

where dimensionless strain-rate parameter h is obtained from h = Sk / e , and S is mean strain rate. h0 is a critical value of dimensionless strain rate and h0 = 4.38 is predefined [17]. Additionally, m and mt are viscosity and turbulent viscosity, respectively. Gk denotes turbulent kinetic energy

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Z1 = 5

Z1 = 7

Z1 = 9

(a) Flow rate of 0.8Q

Z1 = 5

Z1 = 7

Z1 = 9

(b) Flow rate of 1.0Q Fig. 3. Distributions of relative velocity at impeller outlet.

of 0.8Q is associated with apparent reverse flow areas near the impeller hub compared with the condition of nominal flow rate. Meanwhile, the periodicity pertinent to the four impeller blades is well maintained as vane number varies, particularly near the impeller hub. Furthermore, the effect of stator vanes can be perceived near the pump casing and is apparent at flow rate of 0.8Q. As for the 9-vane case, the contribution of stator vanes is obvious at both 0.8Q and 1.0Q. It is therefore deduced that large vane number leads to uniform cross-sectional velocity distributions. Previous results obtained with particle image velocimetry (PIV) also showed that from the impeller hub to the pump casing, axial velocity increases and overall magnitude of axial velocity increases with flow rate. Additionally, with PIV, vortices and recirculation are revealed near the impeller hub and vortices are especially distinct at small flow rates [19]. At stator outlet, the energy transformation capability of stator vanes is well manifested, as shown in Fig. 4. On the whole, the uniformity of axial velocity distribution is enhanced as vane number increases. Furthermore, as vane number in-

creases, reverse-flow areas near the stator hub tend to be annihilated. Flow rate also plays an important part in this connection. An increase in flow rate restricts the development of reverse flows near the pump casing, as applies to the three cases. The most favorable situation surfaces at vane number of 9 and a corresponding flow rate of 1.0Q, while the most adverse situation is evidently related to the 5-vane case at flow rate of 0.8Q. For the latter, the existence of large-scale reverse flow structures which occupy a large portion of cross-sectional area evidently reflects the deficiency of energy transformation.

4. Comparison of operation performance among three pumps Several studies confirmed the connection between flow characteristics and operation performance of the pump, but no robust explanation has been furnished so far [20]. Since some factors such as mechanical loss and leakage loss were not taken into account in numerical simulation, the operation performance of the pump predicted numerically inevitably in-

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Z1 = 5

Z1 = 7

Z1 = 9

(a) Flow rate of 0.8Q

Z1 = 5

Z1 = 7

Z1 = 9

(b) Flow rate of 1.0Q Fig. 4. Absolute velocity distributions at stator outlet.

(a) Variation of pump head with flow rate

(b) Variation of pump efficiency with flow rate

Fig. 5. Operation performance of three axial-flow pumps.

corporated errors. Under such a circumstance, a performance test was carried out on the test platform in Shanghai Kaiquan Pump Group Co., Ltd. Through adjustments and regulations performed on the experimental system, the maximum uncer-

tainties for measurements of pump head and pump efficiency were less than 1% and 1.8%, respectively. Both pump head and pump efficiency were measured for the three pumps with different vane numbers and the results are plotted in Fig. 5.

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(a) Arrangement of monitored points, P1-P4 on the motor base

(c) An overall view of the test rig

(b) Arrangement of monitored points, P1’-P4’,on the supporting plate of the pump

(d) Sketch and image of the pressure hole for pressure fluctuation measurement

Fig. 6. Experimental apparatus for measurements of vibration and pressure fluctuation.

As for the variation of pump head with flow rate shown in Fig. 5(a), it is observable that the three curves do not deviate from each other obviously, although three significantly different sets of stators are being used. Note that for the three cases, a saddle-shape pump head curve segment, a distinct feature of the axial-flow pump, is unanimously found near flow rate of 500 m3/h, namely 0.6Q. Since the three impellers are identical, this experimental result also supports the acknowledged conclusion that reverse flows and circulation near impeller inlet facilitate the saddleshape performance [21]. In regard to the relationship between pump efficiency and flow rate, as illustrated in Fig. 5(b), the 7-vane pump holds the highest efficiency, which corresponds to a flow rate slightly higher than the nominal flow rate. As for the 9-vane pump, the best efficiency point is situated far from the nominal operation condition, and the overall pump efficiency of the 9-vane pump is the lowest among the three pumps. According to the previous discussion, large vane number helps to regulate the flow issuing from the impeller. However, the increase of friction loss occurring concurrently might in turn induce a decline in pump efficiency.

5. Pump vibration and static pressure fluctuations 5.1 Experimental methodology The importance of pump vibration is increasingly being recognized, as is partially attributed to advancement in relevant research techniques [22]. As a subject stressed here, the vibration of the axial-flow pump is analyzed from the perspective of experiment instead of numerical simulation. In the light of conventional pump design principles, pump vibration of a minimum degree is attained at nominal flow rate. Nevertheless, no quantitative verification has been demonstrated even at some given specific speed [23]. Consequently, the contribution of flow parameter distribution or flow pattern to pump vibration has not been substantiated. In the present study, an LMS multi-channel vibration and noise measurement system was used to measure both pump vibration and motor vibration. Sensors for vertical vibration acceleration measurement were attached to specified local surfaces. Monitored points on the motor base, P1 to P4, are shown in Fig. 6(a) and these four points are located on the same horizontal plane. Another four coplanar points, P1’ to P4’, are deployed on the supporting plate of the pump, as shown in Fig. 6(b). The pump equipped with

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Fig. 7. Vibration acceleration level measured on the motor base at nominal flow rate.

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(a) 5-vane case

the 7-vane stator is shown in Fig. 6(c) which also shows the 5vane and 9-vane stators. Aside from overall vibration, transient static pressure fluctuations were measured with several miniature dynamic pressure sensors mounted circumferentially on the pump casing, and these sensors were axially located in the middle of the impeller and the stator. Meanwhile, these sensors were fitted into pressure holes and sensor tips protruded into working medium. One of the pressure holes is shown in Fig. 6(d). The frequency range of 10-8000 Hz was predefined for data acquisition. 5.2 Pump vibration Transiently captured data with the sensors were processed using fast Fourier transformation (FFT) technique, converting time-dependent data into signals in frequency domain. Due to fluctuations of the rotational speed of the impeller due to power frequency fluctuations of the electric power grid, the actually monitored shaft frequency, f, is 24.61 Hz. There is a relative deviation of 1.24% compared with the nominal shaft frequency, which is acceptable as per requirements of ISO 9906:2012. Furthermore, the blade passing frequency (BPF), fz, is 99.22 Hz, which is in accordance with the impeller blade number of 4. In view of the configuration of pump unit components, the four monitored points deployed on the motor base present not just the vibration of the motor itself but also the vibration of the upper part of the pump. However, characteristic frequencies associated with this set of data hinge upon multiple factors and cannot be conveniently predicted. Through data processing, maximum and average values of vibration acceleration level at nominal flow rate are obtained and the results are plotted in Fig. 7. In Fig. 7, for each monitored point, particularly P1, a large gap exists between average value and corresponding maximum value. Such a situation implies that local vibration endures transient fluctuations. Nevertheless, in an average sense, vibration levels at the four monitored points are nearly identi-

(b) 7-vane case

(c) 9-vane case Fig. 8. Vibration acceleration level measured on the supporting plate of the pump.

cal, irrespective of the difference in vane number. It should be stressed that the monitored point P1 is adjacent to the outlet bend of the pump, and the effect of the bend on local vibration should be taken into account. In this context, the deflection of the working medium in the bend and the structure of the bend jointly constitute an influential factor aggravating local vibration. By contrast, the overall vibration level associated with P3

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is comparatively low. As for another two monitored points, P2 and P4, the overall vibration levels well prove the connection between vibration and local position. In addition, Fig. 7 indicates that the influence of vane number on average vibration acceleration level is not remarkable, but the maximum vibration acceleration levels corresponding to the 7-vane case are low compared with their counterparts. As flow rate increased from 0.8Q to 1.2Q with an increment of 0.2Q, vibration acceleration level was measured on the supporting plate of the pump, and the results are plotted in Fig. 8. For all the three cases, the vibration acceleration level values at monitored points P2’ and P4’ are quite close. In this connection, the line covering P2’ and P4’ is perpendicular to the inflow and outflow straight pipes connected to the pump. Therefore, it can be concluded that circumferential balance of the pump is preferable without obvious lateral vibration. Nominal flow rate is associated with minimum vibration, as applies to monitored points P1’ and P3’, although vibration levels at these two points are particularly high. In view of the positions of P1’ and P3’, characteristics of the entire system in which the pump operates contribute apparently to the local vibration considered. In particular, the monitored point P3’, with the highest vibration level, is situated in a diagonal position with respect to the monitored point P1, as shown in Figs. 6(a) and (b). And P3’ is also the nearest point from the inflow pipe. The three cases share similar overall variation tendency of vibration as flow rate increases. And the highest vibration level occurs at 0.8Q. Furthermore, for each case, although vibration acceleration levels at P2’ and P4’ differ, they are not suitable for assessing the influence of flow on vibration acceleration level. Note that at vane number of 9, at P2’ and P4’, variation of vibration acceleration level with flow rate is comparatively regular. 5.3 Pressure fluctuations at 0.8Q As a further exploration, pressure fluctuation between the impeller and the stator is analyzed. The contribution of turbulent fluctuation to the vibration of the whole pump has been highlighted in recent studies [24]. The experimental system used in this study enables the measurement of time-dependent static pressure fluctuations with a high fidelity. In accordance with the main aim of the present study, static pressure fluctuations in the flow region between the impeller and the stator serve as an indicator of turbulent flow features, which are sensitive to the effect of vane number. By using fast Fourier transformation, pressure fluctuations in frequency domain at flow rate of 0.8Q were obtained and plotted in Fig. 9. For all the three cases, blade passing frequency and its harmonics dominate the frequency spectra, as evidenced in Fig. 9. In comparison, shaft frequency and its harmonics can only be identified through some considerably low peaks of pressure fluctuation amplitude. These transient pressure fluctuations obtained demonstrate that the rotation of the impeller is highly influential even at small time scales. Also shown in Fig. 9, for

Fig. 9. Pressure fluctuations between the impeller and the stator at 0.8Q.

all the three cases, high-frequency components within the displayed frequency range are discretely distributed. In general, small-scale flow structures stimulate the emergence of high-frequency components [25]. At high frequencies, the 9vane case incorporates high amplitudes of pressure fluctuations compared with the other two cases. This is inseparable from the prevalence of small flow structures at vane number of 9. In addition, these high frequencies are still multiples of blade passing frequency. For each case, low peaks are present among high pressure fluctuation amplitude peaks, as is particularly clear at vane number of 9. The overall pressure fluctuation amplitude of the 7-vane case is lower than its counterparts. Meanwhile, the similarity between the frequency spectra of the 5-vane and 7-vane cases is easily recognizable, while the frequency spectrum of the 9vane case is quite different. From another perspective, the combination of five stator vanes and four impeller blades boosts the formation of large-scale flow structures, which offer little support to high-frequency pressure fluctuations. Additionally, for the 9-vane case, periodic interaction between impeller blades and stator vanes is frequent and intense, irrespective of the uniformity of velocity distribution. In Ref. [6], it is suggested that large discrepancy in periodicity, such as the situation of four impeller blades along with nine stator vanes, enhances flow-induced pump vibration. 5.4 Pressure fluctuations at 1.0Q Pressure fluctuations at nominal flow rate are illustrated in Fig. 10. And the maximum pressure fluctuation amplitude occurs invariably at blade passing frequency; overall pressure fluctuations are appreciably suppressed compared with Fig. 9. In regard to the 5-vane case, the two pressure fluctuation spectra corresponding to 0.8Q and 1.0Q are highly analogous. Nevertheless, the pressure fluctuation amplitude at blade passing frequency decreases sharply from about 20 kPa to 12.5 kPa. Furthermore, discrete peaks of pressure fluctuations

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cases. Compared with the other two cases, the 7-vane case has relatively low characteristic pressure fluctuation amplitudes. As flow rate increases from 0.8Q to 1.0Q, all characteristic pressure fluctuation amplitudes decline with the 5-vane case, while the 9-vane case is featured by active low-order harmonics together with decayed high-frequency components.

Acknowledgments

Fig. 10. Pressure fluctuations between the impeller and the stator at 1.0Q.

This study is financially supported by the project funded by College Industrialization Project of Jiangsu Province (Grant No.JHB2011-37) and Priority Academic Program Development of Jiangsu Higher Education Institutions. The authors would extend their gratitude to all colleagues and graduate students actively involved in the experimental work.

Nomenclature-----------------------------------------------------------------------among harmonics of blade passing frequency are maintained. In contrast, the other two cases, especially the 9-vane case, experience an overall change as flow rate increases. For the 7vane case, all pressure fluctuation amplitudes decrease as flow rate increases, while the pressure fluctuation amplitude corresponding to blade passing frequency varies slightly. A distinct characteristic pertinent to the 7-vane case is that most highfrequency components are restrained or even eliminated as flow rate increases from 0.8Q to 1.0Q. Concerning the 9-vane case, many high-frequency components arising at 0.8Q are suppressed. Additionally, harmonic frequencies of fz are active at vane number of 9, as cannot evade from the influence of local flow patterns. This connection has not been detailed since correlations among flow structures have not been established due to lack of turbulence data.

6. Conclusions Vane number affects both energy transformation capability and inner flow characteristics of the axial-flow pump. Pump head curves associated with the three vane number cases are in modest agreement, while the 7-vane case proves to be the most preferable one in terms of pump efficiency. The 9-vane case has the lowest overall pump efficiency. Nevertheless, large vane number facilitates the rise in velocity distribution uniformity at both impeller outlet and stator outlet. Variation in vane number accounts for an insignificant change in terms of pump vibration. Apart from the circumferentially even vibration monitored on the motor base, high vibration level arises at two local positions on the supporting plate: one is near the outlet bend of the pump and the other is adjacent to the inflow pipe. Both structural and hydraulic factors are pivotal in this context. At nominal flow rate, minimum pump vibration level is manifested. Frequency spectra of pressure fluctuations between the impeller and the stator are overwhelmingly dominated by blade passing frequency and its harmonics, as is shared by the three

fz H k n ns Q Z Z1 ε

: Blade passing frequency : Pump head : Turbulent kinetic energy : Rotational speed : Specific speed : Volume flow rate : Impeller blade number : Stator vane number : Turbulent kinetic energy dissipation rate

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Can Kang received his Ph.D. from the Jiangsu University of China. He is an associate professor and Ph.D. supervisor at the Jiangsu University of China. His research interests include optimal design of impeller pumps, non-intrusive flow measurement, high-pressure water jet and cavitation in aerated flows.